Perimeter of Triangle: The perimeter of any two-dimensional figure is defined as the distance around the figure. We can calculate the perimeter of any closed shape just adding up the length of each of the sides. In this article, you will first learn about what is the perimeter, how to find the perimeter of different types of triangles when all side lengths are known. Furthermore, the solved examples will help you to get more views on the topic.
What is the Perimeter of a Triangle?
The sum of the lengths of the sides is the perimeter of any polygon. In the case of a triangle,
Perimeter = Sum of the three sides
Always include units in the final answer. If the sides of the triangle are measured in centimetres, then the final answer should also be in centimetres.
Perimeter of Triangle Formula
The formula for the perimeter of a closed shape figure is usually equal to the length of the outer line of the figure. Therefore, in the case of a triangle, the perimeter will be the sum of all the three sides. If a triangle has three sides a, b and c, then,
Perimeter, P = a + b +c
Perimeter of an Isosceles, Equilateral and Scalene Triangle
Below table helps us to understand how to find the perimeter of different triangles- Equilateral triangle, Isosceles triangle and Scalene triangle.
This formula implies to find the perimeter of a triangle, add the lengths of all of its 3 sides together. If A, B and C are the side measures, and X is perimeter then
Perimeter of Right Triangle
A right triangle has a base(b), hypotenuse(h) and perpendicular(p) as its sides, By the Pythagoras theorem, we know,
h2 = b2 + p2
Therefore, the Perimeter of a right angle triangle= b + p + h
Video Lesson on Triangles
Let us consider some of the examples on the perimeter of a triangle:
Example 1: Find the perimeter of a polygon whose sides are 5 cm, 4 cm and 2 cm.
a = 5 cm
b = 4 cm
c = 2 cm
Perimeter = Sum of all sides = a + b + c = 5 + 4 + 2 = 11
Therefore, the answer is 11 cm.
Example 2: Find the perimeter of a triangle whose each side is 10 cm.
Solution: Since all three sides are equal in length, the triangle is an equilateral triangle.
i.e. a = b = c = 10 cm
Perimeter = a + b + c
= 10 + 10 + 10
Perimeter = 30 cm.
Example 3: What is the missing side length of a triangle whose perimeter is 40 cm and two sides are 10 cm each?
Perimeter = 40 cm
Length of two sides is the same i.e. 10 cm.
Thus, the triangle is an isosceles triangle.
Using formula: P = 2l + b
40 = 2 * 10 + b
40 = 20 + b
or b = 20
Missing side length is 20 cm.
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|Perimeter of a Triangle Formula||Equilateral Triangle Formula|
|Types of Triangles||Scalene Triangle|
|Acute angled Triangle||Isosceles Triangle Perimeter Formula|
Frequently Asked Questions
What does the Perimeter of a Triangle Mean?
The perimeter of a triangle is the total distance around the edges of a triangle. In other words, the length of the boundary of a triangle is its perimeter.
How to Calculate the Perimeter of a Triangle?
To calculate the perimeter of a triangle, add the length of its sides. For example, if a triangle has sides a, b, and c, then the perimeter of that triangle will be P = a + b + c.
Calculate the Perimeter of a Right Triangle with Base as 3 cm and height as 4 cm.
First, using the Pythagorean theorem, calculate the hypotenuse of the right triangle.
h = √(32+42)
h = √(9 + 16)
h = √25
Or, h = 5 cm
So, the perimeter of the triangle = 3 + 4 + 5 = 12 cm.
How to calculate the perimeter of a scalene triangle?
If x, y, and z are the sides of a scalene triangle, then its perimeter formula is given by:
Perimeter of a scalene triangle, P = x + y + z units.
What is the formula for the perimeter of an isosceles triangle?
As we know that the isosceles triangle has 2 equal sides, then the formula for the perimeter of an isosceles triangle is given as P = 2x + y units,
where “x” is the measure of equal sides of a triangle and “y” is the third side.
What is the formula for the perimeter of an equilateral triangle?
In an equilateral triangle, all the sides are equal. Let the side length of an equilateral triangle be “x”.
Thus, the perimeter of an equilateral triangle is = 3x units.
Calculate the perimeter of an equilateral triangle if its side measures 5 cm.
Given: Side measure of equilateral triangle = 5 cm.
Now, substitute the side value in the perimeter of an equilateral triangle formula, we get
P = 3 (5) = 15 units.
Find the perimeter of a triangle whose sides are 3 cm, 4 cm and 6 cm.
We know that the perimeter of a triangle = x + y + z units
Hence, P = 3 + 4 + 6 = 13 cm.
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